A beach house in southern California now costs $350,000. Inflation is expected to cause this price to increase at 5 percent per year over the next 20 years before Eric and Karinna retire from successful careers in commercial art. How large an equal annual end-of-year deposit must be made into an account paying an annual rate of interest of 13 percent in order to buy the beach house upon retirement?

Question

Quizplus · Accepted Answer

The future value of the beach house is given by:
FV = PV * (1 + i)^n = $350,000 * (1 + 0.05)^20 = $1,140,232.78
The amount of the annual deposits needed to accumulate this future value can be calculated using the formula for the future value of an annuity:
FV = PMT * [(1 + i)^n - 1] / i, where PMT is the annual deposit.
Substituting the given values, we get:
$1,140,232.78 = PMT * [(1 + 0.13)^20 - 1] / 0.13
Solving for PMT, we get:
PMT = $11,471.10, which is the required annual deposit.

Therefore, the best choice is A.

A Beach House in Southern California Now Costs $350,000